So in this diagram, we're going to visualize the process of revenue coming in

from a particular customer and I encourage you perhaps even to draw a diagram of this

sort for your own customers in your own business.

So let's assume a fairly simply example,

that the business that we're running is something like a mobile phone service and

that every year, the customer is spending $250 with us in terms of the net margin.

So the revenue may be a little bit higher minus some costs that we have of

variable costs maintaining that customer, we're getting $250 at margin.

Now, in addition, that cost is $400 in the beginning to acquire the customer.

Perhaps we had to give them a free cellular phone or something like that.

So, with this information in hand, over five periods, so

that's the lifetime that we're assuming that the customer is going to live for.

We can start to execute on the calculation of customer lifetime value.

So, let's go through this and do it together.

And let's do it in a very, very simple sense, so

we'll assume that there's no customer attrition.

Wow, wouldn't that be a great business.

The customer never leaves us,

stays with us with probability one every period for five years.

Secondly, let's assume that we're not going to do any discounting in

the calculation, that the money that we receive from the customer in year five

is just as valuable as the money that we receive in year one.

Of course our finance colleagues would not like us to make such an assumption, so

we'll modify that shortly.

But le's go ahead and do the calculation.

So, in this case, the customer lifetime value is just the five increments of $250

at margin, $1250 minus the acquisition cost

of $400 which leaves a net customer lifetime value of $850.

So the reason I'm showing you this example is as we start to layer in other things

like attrition and discount rate, what you'll notice is

that the customer's lifetime value the number starts to decline.

And it starts to decline quite dramatically so for

those of you who are students of business history which I hope many of you are,

if you think about things like the Internet boom and bust ,there are a lot of

companies during the 1.0, maybe still even today, that were grossly over valued or

grossly optimistic about what the value of the enterprise was because they made some

rather heroic assumptions about the values of their customers.

Either the margin that they were getting every period or the chance that

the customers would actually stay with the business and be retained, so.

That's one important point that I want you to look for, even in this very,

very simple example.

Just to see how dramatically the value is going to change

as we start to relax those assumptions.

So, let's go ahead and do that.

And so, now let's turn again to our familiar diagram where we have the flow

of margin coming in from the customer every period, but

this time around we're going to add one additional assumption,

which is that customers, unfortunately, might decide to leave us.

There's going to be some probability of attrition that's going to

cause the customer lifetime value number that we ultimately calculate to go down.

Now, this is something that actually is quite subtle and quite important.

And for those of you who are students of business history, which I hope many of you

are, if you think back to the boom and bust of things like Web 1.0,

part of the reason that happened is that people made gross overstatements or

grossly misstated assumptions about what the value of different businesses were.

Based on the underlying customer transactions and the underlying customer

asset in particular, they either assume that the margin that was going to

come in from the customer was much higher than what it turned out to

be because the customers couldn't be monetized in the way people thought.

Or the entrepreneurs though that the chance of retaining

customers was much higher than it actually was,

because they discounted the fact that a competitor could steal a customer, or

a customer might just leave of natural causes, doesn't really find the value in

the service that we, as the entrepreneurs would like to believe that they have.

And what you'll notice here, this is a very important element of the customer

lifetime value calculation is that even a fairly small degradation in the retention

rate can have a dramatic effect on the number that ultimately get's calculated.

So, lets go through and do this, and

then the example, we're going to assume a retention rate of 80%.

Now that's actually a pretty good number.

So, I think we'd be fairly pleased as your colleagues and

instructors in this course if there was a 80%chance from week to week that you

kept engaged with the class and applying the materials.

What we'll see however, is even with an 80% retention rate,

there's going to be quite a dramatic reduction in the value that we got

from the model previously, the value previously, was a total of $850.

Where we would assume customers would always stay with us.

For five years, and we also assume no time value of money,

we'll get to that one in a second.

So, what we're also going to do here, is you notice in the calculation is that at

the end of every period, the customer can either leave with probability 0.2,

or stay with probability 0.8, and

this process gets repeated until the end of the 5th period.

Now, those of you who're sort of looking at the slide,

there are those of you have studied a little bit of statistics in mathematics,

might say, hang on a minute, there's quite a simplifying assumption here.

You've assumed that the probability that the customer is there by the end of

year 2 is 0.8, at the end of year 3 is just 0.8 squared,

at the end of year 4 is 0.8 cubed.

So implicitly I've assumed

that the retention rates are independent from one year to the next.

Which seems like a pretty unrealistic, shall we say, assumption.

But, let's go back to where we started our session today,

with the notion that all models are wrong.

Thank you.

But some are useful.

So clearly it's a bit of an unrealistic assumption but it's made not only just for

mathematical convenience but

also because it may not in fact be such a bad assumption after all.

So imagine that my colleague Stephanie is a customer of AT&T.

The longer she stays with AT&T we might argue that her retention rates going up,

she likes the service, she's getting used to it,

she really doesn't want to go anywhere else.

At the same time, there could be other factors

causing her retention rate to be potentially going down.

Competitors like Verizon chasing after her.

She's just getting a little bit tired of the service, and so on.

So, as my colleague and friend, Sunil Gupta,

at Harvard Business School might argue,

there are forces pushing retention rates up, there are forces pushing them down.

So assuming that they're roughly constant, is not such a bad thing to do.

Now of course, getting the right number in the first place by doing as I said before,

looking at a cohort that entered at the same time period and

asking how many remained after a certain point through time

to calculate the retention rate that's probably the most critical thing of all.

So let's go through now and do the numbers.

I'm now just computing the expected contribution which is

the margin modified by the retention rate.

So I've done that there in the slide.

We add all those numbers up.

We get a net value now of $840, not $1250, and of course we have to

subtract out the initial acquisition cost, which I just assumed to be $400.

So now we have a customer lifetime value of $440.

Wow, that's a big drop from $850.

So you can imagine why this retention rate is just so critical.

In fact, the academic research suggests of all the four elements in

the mathematical formula, the one that produces the most leverage or

impact over the final number that you calculate is in fact the retention rate so

always be wary of somebody who's making an assumption about retention.

That's just too heroic or too unrealistic.

Because if they're doing that they're going to be grossly over estimating

the value of individual customers so as entrepenuers we always want to err

on the side of caution and off course to sensitivity.

Let's see what the result looks like if we assume 90%, or 80%, or 70%, and so on.

So we now have completed the second calculation, let's continue on, and

do a third one.

And so now on the screen in front of us we have the familiar flow diagram of,

margin coming in every period from the customer for five periods.

We also have on top of that the retention factor,

which we assumed in the beginning that they are with probability one.

And then in every period they have a chance of 80% of staying with us

20% of leaving, and on top of that I've computed the expected contribution,

$250 dollars, $200 dollars, $160 and so on down.

Now in this case we are just going to have one final component, which is something

that our finance colleagues, or your CFO at your start up, or your venture would

be really concerned about, which is of course the time value of money.

So we're retaining the assumption that customers will be with us,

with probability 80%.

So they'll churn or we'll lose them with probability 0.2.

In addition let's just assume that the value of money that comes in

is not as valuable in the future as it is in the present.

That's a pretty good assumption.

And let's have a discount rate of 10% just to make the math easy and

now let's go through and do that calculation so

the discount factor that's applied to the first piece of money that comes in at

the end of year one is just one divided one plus the discount factor which is 10%.

At the end of two years that's just again,

one, divided by one

plus the discount rate 10%, and

then we square the whole thing, and then we cube and so on.

What we see is we get now a value of $664.

We subtract out the $400 to acquire the customer.

Wow, almost nothing left.

We're down to $264.

So just think about this for a moment.

We've done a very, very simple and very stripped down example.

I really hope that you're going through and

thinking about your own customers in applying the same kind of logic and

we started with a customer lifetime value of $850.

We're now down to a number that's roughly about a third of that even with having

what seems to be a pretty good retention rate.

And also applying a fairly modest discount rate of

about 10% to the time value of money.

So, we can see that when one starts to really build in some more realistic

assumptions about whether or not customers will be retained and

the value of revenue that we might be getting in the future.

When you do those two things, you end up with a dramatically lower number.

That's really the bottom line here.

So, with this in mind, I'm now going to give you a couple of quick and

dirty simple ways to do this calculation without going through and

doing the adding up from every single period.

And also talk about some extensions that I would really love for some of you

to do for your homework, if you really need to dig a little bit deeper, and

go into a more sophisticated approach.

So now let me just give you one other very simple way,

just in a very rough sense, to calculate customer lifetime value.

In the examples that we just went through, remember that the customer

was sticking around for five periods, five years in our example.

We only added up the data for a period of five.

Let's imagine now however that the customer keeps on going, period six,

period seven, period eight, but

of course in every period, the chance that they stick around is declining,

declining, so it would be 0.8 to the five, 0.8 to the six and so on.

So, if we do then, we make that assumption that the customer is, in some sense,

almost going to be around forever, but with the declining chance every period.

So, in this case the customer lifetime value is simply the return, or the margin

divided by the churn rate, the churn rate is 0.2 or 1 minus the retention rate.

That gives us 1,250.

Subtract off the $400 acquisition cost.

If we wanted to then modify the formula again, assuming that the customer

is not there for five periods but six, seven, eight, keeps on going.

It's just going to be the margin $250 divided by the churn rate,

0.2 + the discount rate of 0.1.

So these are some really simple heuristics that you can use to apply to

to different customers to see which ones are more valuable, which ones are less so.

And of course, in all of these cases, whether you do the summing up.

Over a certain number of periods, or whether you use the direct formula

assuming that the customer is always going to be around.

Always be critical as entrepreneurs about the assumption around retention.

And always try to do some experimentation or some sensitivity.